Quinn, 28, was released by the Seattle Seahawks in final cuts on Saturday after losing a battle with Tarvaris Jackson for the team's backup quarterback role. Prior to joining the Seahawks, Quinn was with the Kansas City Chiefs in 2012, where he started eight games.
A first-round pick in the 2007 NFL Draft, the Jets are the fifth team for Quinn and the fourth in the last two years. In 24 career games, Quinn has accumulated 3,043 yards passing, 12 touchdowns, 17 interceptions and a 64.4 career passer rating.
The Jets currently have four quarterbacks, although Mark Sanchez isn't expected to be ready for the beginning of the regular season after injuring his shoulder in preseason. Instead it will be rookie second-round pick Geno Smith likely making the start for the Jets in Week 1, with Matt Simms and Quinn fighting for the backup role.